2-point Correlations Research Articles

Effect of laser scan rotation on the microstructure and mechanical properties of laser powder bed fused Haynes 282

Haynes 282 is a weldable, γ′ strengthened Ni-based superalloy and is a suitable candidate for aerospace and power-generation applications. Laser powder bed fusion (LPBF) of Haynes 282 is gaining attention recently due to its superior mechanical properties than its conventional counterparts. In spite of the superior mechanical properties, there are significant challenges concerning crystallographic anisotropy. One of the critical but less studied parameters that influence crystallographic anisotropy is the laser scan rotation angle. This study investigates the effect of laser scan rotation angle on the microstructure and subsequently on the mechanical properties. The samples fabricated with 90° scan rotation exhibited stronger texture while the samples with 137° rotation had weaker texture than samples with 67°. Further, three-dimensional Finite difference-Monte Carlo simulations were performed to understand the microstructure evolution with varying process parameters. The experimental and simulated microstructures are quantitatively compared using 2-point correlations. The texture and grain morphology evolution are explained based on melt pool morphology and microstructure simulations. Mechanical properties of as-built and aged samples are estimated using theoretical models and agree well with the experimental results.

Angular correlations on causally-coherent inflationary horizons

We develop a model for correlations of cosmic microwave background (CMB) anisotropy on the largest angular scales, based on standard causal geometrical relationships in slow-roll inflation. Unlike standard models based on quantized field modes, it describes perturbations with nonlocal directional coherence on spherical boundaries of causal diamonds. Causal constraints reduce the number of independent degrees of freedom, impose new angular symmetries, and eliminate cosmic variance for purely angular 2-point correlations. Distortions of causal structure from vacuum fluctuations are modeled as gravitational memory from randomly oriented outgoing and incoming gravitational null shocks, with nonlocally coherent directional displacements on curved surfaces of causal diamonds formed by standard inflationary horizons. The angular distribution is determined by axially symmetric shock displacements on circular intersections of the comoving sphere that represents the CMB photosphere with other inflationary horizons—those centered on it, and those that pass through an observer’s world line. Displacements on thin spheres at the end of inflation have a unique angular power spectrum that approximates the standard expectation on small angular scales, but differs substantially at large angular scales due to horizon curvature. For a thin sphere, the model predicts a universal angular correlation function with an exact ‘causal shadow’ symmetry, , and significant large-angle parity violation. We apply a rank statistic to compare models with WMAP and Planck satellite data, and find that a causally-coherent model with no shape parameters or cosmic variance agrees with the measured better than a large fraction () of standard model realizations. Model-independent tests of holographic causal symmetries are proposed.

Reduced-Order Models Correlating Ti Beta 21S Microstructures and Vickers Hardness Measurements

Ti Beta 21S alloy is a metastable Ti Beta alloy commonly used in the aerospace industry, especially in jet engines. Components made from this alloy are usually subjected to various thermal histories during service, which leads to significant changes in their microstructures and associated mechanical properties. The central goal of this study is to demonstrate the feasibility of correlating the optical images of the microstructure obtained from heat-treated samples of Ti Beta 21S to their respective Vickers hardness measurements using recently established analyses and statistical quantification approaches based on the principal components of the rotationally invariant 2-point spatial correlations. The correlations extracted in this work can be used for non-destructive diagnostics of in-service components.

Correlations of the Thue–Morse sequence

The pair correlations of the Thue–Morse sequence and system are revisited, with focus on asymptotic results on various means. First, it is shown that all higher-order correlations of the Thue–Morse sequence with general real weights are effectively determined by a single value of the balanced 2-point correlation. As a consequence, we show that all odd-order correlations of the balanced Thue–Morse sequence vanish, and that, for any even n, the n-point correlations of the balanced Thue–Morse sequence have mean value zero, as do their absolute values, raised to an arbitrary positive power. All these results also apply to the entire Thue–Morse system. We finish by showing how the correlations of the Thue–Morse system with general real weights can be derived from the balanced 2-point correlations.

Machine learning and materials informatics approaches for predicting transverse mechanical properties of unidirectional CFRP composites with microvoids

The mechanical properties of composites are traditionally measured using numerical and experimental approaches, which impede the innovation of materials due to the cost, time, or effort involved. This study for the first time develops a machine learning-assisted model, which aims at predicting the transverse mechanical properties of unidirectional (UD) carbon fiber reinforced polymer (CFRP) composites with microvoids. To this end, the stochastic microstructures are generated by random sequential expansion (RSE) and hard-core model. And the transverse elastic modulus, transverse tensile strength and transverse compressive strength are computed by micromechanics-based finite element (FE) method. Then, the reduced order representation of microstructures is determined using 2-point spatial correlations and principal component analysis (PCA). Finally, a genetic algorithm (GA) optimized back propagation (BP) neural network is implemented to capture the potential nonlinear relationship between microstructure and transverse mechanical properties. The presented data-driven techniques can reproduce the FE simulation results with an R-value of 0.89 or greater. The excellent agreement between the predicted results and test datasets verifies the successful application of data science methodologies in elucidating the microstructure-property linkages of UD-CFRP composites with microvoids, and thus provides a promising tool for accelerating the smart design and optimization of composites.

Dark Energy Survey Year 3 results: Cosmology with moments of weak lensing mass maps

We present a cosmological analysis using the second and third moments of the weak lensing mass (convergence) maps from the first three years of data (Y3) data of the Dark Energy Survey. The survey spans an effective area of 4139 square degrees and uses the images of over 100 million galaxies to reconstruct the convergence field. The second moment of the convergence as a function of smoothing scale contains information similar to standard shear 2-point statistics. The third moment, or the skewness, contains additional non-Gaussian information. The data is analyzed in the context of the ΛCDM model, varying five cosmological parameters and 19 nuisance parameters modeling astrophysical and measurement systematics. Our modeling of the observables is completely analytical, and has been tested with simulations in our previous methodology study. We obtain a 1.7% measurement of the amplitude of fluctuations parameter S8≡σ8(Ωm/0.3)0.5=0.784±0.013. The measurements are shown to be internally consistent across redshift bins, angular scales, and between second and third moments. In particular, the measured third moment is consistent with the expectation of gravitational clustering under the ΛCDM model. The addition of the third moment improves the constraints on S8 and Ωm by ∼15% and ∼25% compared to an analysis that only uses second moments. We compare our results with Planck constraints from the cosmic microwave background, finding a 2.2–2.8σ tension in the full parameter space, depending on the combination of moments considered. The third moment, independently, is in 2.8σ tension with Planck, and thus provides a cross-check on the analyses of 2-point correlations.13 MoreReceived 13 November 2021Accepted 30 August 2022DOI:https://doi.org/10.1103/PhysRevD.106.083509© 2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCosmological parametersCosmologyGravitation, Cosmology & Astrophysics

Trans-IR flows to black hole singularities

We study analytic continuations of holographic renormalization group (RG) flows beyond their infrared (IR) fixed points. Such ``trans-IR'' flows are a natural framework for describing physics inside of black holes. First, we construct a monotonic holographic $a$-function which counts degrees of freedom along a trans-IR flow. Using this function, we argue that the degrees of freedom ``thin out'' and vanish when flowing to a trans-IR endpoint, represented by a Kasner singularity. We then recast well-studied quantum information probes in the language of trans-IR flows, finding that entanglement and complexity from volume generally fail to fully probe the trans-IR while 2-point correlations and complexity from action generally do so in a complementary manner.

Random singlet-like phase of disordered Hubbard chains

Local moment formation is ubiquitous in disordered semiconductors such as Si:P, where it is observed both in the metallic and the insulating regimes. Here, we focus on local moment behavior in disordered insulators, which arises from short-ranged, repulsive electron-electron interactions. Using density matrix renormalization group and strong-disorder renormalization group methods, we study paradigmatic models of interacting insulators: one dimensional Hubbard chains with quenched randomness. In chains with either random fermion hoppings or random chemical potentials, both at and away from half-filling, we find exponential decay of charge and fermion 2-point correlations but power-law decay of spin correlations that are indicative of the random singlet phase. The numerical results can be understood qualitatively by appealing to the large-interaction limit of the Hubbard chain, in which a remarkably simple picture emerges.

Feature Engineering for Microstructure–Property Mapping in Organic Photovoltaics

Linking the highly complex morphology of organic photovoltaic (OPV) thin films to their charge transport properties is critical for achieving high performance material systems that facilitate cost-efficient energy harvesting. In this paper, the current Materials Knowledge Systems (MKS) framework was extended so that it was able to establish reduced-order high-fidelity structure–property linkages for OPV films. Specifically, the following extensions were needed: (i) the proper application of digital image processing algorithms to identify the salient local material states in OPV microstructures controlling the charge transport phenomenon, (ii) computationally efficient feature engineering that not only utilized 2-point spatial correlations and principal component analysis, but also two new distance-based metrics, and (iii) the successful application of a localized version of the Gaussian process (laGP) together with an active learning Cohn (ALC) for building the desired surrogate models linking the OPV microstructures to their short-circuit currents. It is demonstrated that the extended MKS framework can produce high-fidelity structure–property linkages for OPV films.

An Ergodic Theorem for Quantum Processes with Applications to Matrix Product States

Any discrete quantum process is represented by a sequence of quantum channels. We consider ergodic quantum processes obtained by a map that takes the points along the trajectory of a discrete ergodic dynamical system to the space of quantum channels. Under a natural irreducibility condition, we obtain a theorem showing that the state under such a process converges exponentially fast to an ergodic sequence depending on the process, but independent of the initial state. As an application, we describe the thermodynamic limit of ergodic matrix product states and prove that the 2-point correlations of local observables in such states decay exponentially with their distance in the bulk.

Materials informatics of woven fabric composites: Effect of different dimensionality reduction and learning methods

A microscale data-driven framework, under the emerging Materials Informatics paradigm, is developed to build structure-property linkages of woven composites. To show the approach, the microstructure of a set of glass fiber-reinforced polymer samples are imaged using micro-computed tomography, with the property of interest being the elastic modulus obtained from tensile tests. After data collection, fingerprints of microstructural images are calculated by means of 2-point spatial correlations. Different dimensionality reduction algorithms are next employed and compared to build reduced-order representations of the ensuing heatmaps and subsequently identify the dominant features for each composite sample through the Least Absolute Shrinkage and Selection Operator (LASSO) regularization. The tested dimensionality reduction algorithms include Principal Component Analysis (PCA), Non-negative Matrix Factorization (NMF), and Partial Least Squares (PLS). Using the dominant features, different structure-property surrogate models are built and compared via a set of common machine learning techniques: Multiple Linear Regression (MLR), Random Forest Regression (RFR), Support Vector Regression (SVR), and Gaussian Process Regression (GPR). In addition, a Linear Mixed-effect Model (LMM) is developed to account for potential random effects taking place during the fabrication of samples. In this case study, the best performing models were RFR and PLS, with the latter containing components well correlated with the material geometrical attributes such as fiber orientation and fiber volume fraction. This preliminary Composites Informatics case study would furnish the path for a non-destructive property-microstructure prediction of woven fabrics, as well as data-driven discovery and design of new reinforcements.

Development of a Robust CNN Model for Capturing Microstructure-Property Linkages and Building Property Closures Supporting Material Design

Recent works have demonstrated the viability of convolutional neural networks (CNN) for capturing the highly non-linear microstructure-property linkages in high contrast composite material systems. In this work, we develop a new CNN architecture that utilizes a drastically reduced number of trainable parameters for building these linkages, compared to the benchmarks in current literature. This is accomplished by creating CNN architectures that completely avoid the use of fully connected layers, while using the 2-point spatial correlations of the microstructure as the input to the CNN. In addition to increased robustness (because of the much smaller number of trainable parameters), the CNN models developed in this work facilitate the construction of property closures at very low computational cost. This is because it allows for easy exploration of the space of valid 2-point spatial correlations, which is known to be a convex hull. Consequently, one can generate new sets of valid 2-point spatial correlations from previously available valid sets of 2-point spatial correlations, simply as convex combinations. This work demonstrates the significant benefits of utilizing 2-point spatial correlations as the input to the CNN, in place of the voxelated discrete microstructures used in current benchmarks.

Reduced-order models for microstructure-sensitive effective thermal conductivity of woven ceramic matrix composites with residual porosity

This paper presents a data-driven framework for the development of reduced-order models to predict microstructure-sensitive effective thermal conductivity of woven ceramic matrix composites (CMCs) with residual porosity. The main components of the proposed framework include (i) digital generation of representative volume elements (RVEs), (ii) estimation of the effective thermal conductivities of the RVEs using finite element (FE) models, (iii) low dimensional representation of the microstructure in the RVEs using 2-point spatial correlations and principal component analysis (PCA), and (iv) an active learning strategy based on Gaussian process regression (GPR) that minimizes the size of the training dataset through the selection of microstructures with the highest potential for information gain. The reduced-order models are demonstrated to provide high fidelity predictions on new RVEs.

Machine learning approaches for feature engineering of the crystal structure: Application to the prediction of the formation energy of cubic compounds

In this study, we present an approach (along with the needed computational strategies) for efficient and scalable feature engineering of the crystal structure in compounds of different chemical compositions. This approach utilizes a versatile and extensible framework for the quantification of a three-dimensional voxelized crystal structure in the form of 2-point spatial correlations of multiple atomic attributes and performs principal component analysis to extract the low-dimensional features that could be used to build surrogate models for material properties of interest. An application of the proposed feature engineering framework is demonstrated on a case study involving the prediction of the formation energies of crystalline compounds using two vastly different surrogate model building strategies; local Gaussian process regression and neural networks. Specifically, it is shown that the top 25 features (i.e., principal component scores) identified by the proposed framework serve as good regressors for the formation energy of the crystalline substance for both model building strategies.

Replacing the Notion of Spacetime Distance by the Notion of Correlation

Spacetime is conventionally viewed as a stage on which actors, in the form of massive and massless matter, move. In this study, we explore what may lie beyond this picture. The starting point is the observation that quantum field fluctuations are the more strongly correlated the shorter their spacetime distance. The notion of spacetime distance can, therefore, be replaced by the notion of correlation strength. This suggests a new picture in which the abstract 2-point and multi-point correlations are the primary structure, a picture which is essentially information-theoretic. In the low energy regime, the secondary notions of spacetime and of matter would then emerge as approximate representations of the abstract correlators, namely, in the form of Feynman rules on curved spacetime.

Digital Representation and Quantification of Discrete Dislocation Structures

Dislocation networks and their evolution are known to control the mechanical properties of metal samples. However, the lack of computationally efficient and statistically rigorous descriptors for such defect systems has hindered the development and adoption of rational protocols for the optimal design of these material systems. This study presents a framework for the rigorous statistical quantification and low dimensional representation of dislocation networks using the formalism of 2-point spatial correlations (also called 2-point statistics) along with Principle Component Analysis (PCA). The usefulness of this basic framework for comparing and observing dislocation networks is exemplified and discussed with suitable examples.

A machine learning framework for the temporal evolution of microstructure during static recrystallization of polycrystalline materials simulated by cellular automaton

Reduced-order models of process-structure evolution linkages play a central role in the discovery and development of new/improved materials and their deployment in advanced technologies. In this paper, a novel machine learning framework is developed for capturing the temporal evolution of microstructures during static recrystallization of face-centered cubic (FCC) polycrystalline materials and is demonstrated on a collection of simulation data produced using cellular automata. This new framework first establishes a suitable low-dimensional representation of the polycrystalline microstructures based on 2-point spatial correlations expressed in a generalized spherical harmonics (GSH) basis. Second, a Gaussian process autoregression (GPAR) time-series modeling approach is employed to establish the desired reduced-order process-structure evolution model. It is demonstrated that the framework presented in this paper produces remarkably accurate and robust reduced-order models for the problem studied, in spite of the highly complex three-dimensional (3-D) microstructures involved.

BAO signatures in the 2-point angular correlations and the Hubble tension

An observational tension on estimates of the Hubble parameter, H_0, using early and late Universe information, is being of intense discussion in the literature. Additionally, it is of great importance to measure H_0 independently of CMB data and local distance ladder method. In this sense, we analyze 15 measurements of the transversal BAO scale, theta _mathrm{BAO}, obtained in a weakly model-dependent approach, in combination with other data sets obtained in a model-independent way, namely, Big Bang Nucleosynthesis (BBN) information, 6 gravitationally lensed quasars with measured time delays by the H0LiCOW team, and measures of cosmic chronometers (CC). We find H_0 = 74.88_{-2.1}^{+1.9} km s{}^{-1} Mpc{}^{-1} and H_0 = 72.06_{-1.3}^{+1.2} km s{}^{-1} Mpc{}^{-1} from theta _{BAO}+BBN+H0LiCOW and theta _{BAO}+BBN+CC, respectively, in fully accordance with local measurements. Moreover, we estimate the sound horizon at drag epoch, r_mathrm{d}, independent of CMB data, and find r_mathrm{d}=144.1_{-5.5}^{+5.3} Mpc (from theta _{BAO}+BBN+H0LiCOW) and r_mathrm{d} =150.4_{-3.3}^{+2.7} Mpc (from theta _{BAO}+BBN+CC). In a second round of analysis, we test how the presence of a possible spatial curvature, Omega _k, can influence the main results. We compare our constraints on H_0 and r_mathrm{d} with other reported values. Our results show that it is possible to use a robust compilation of transversal BAO data, theta _{BAO}, jointly with other model-independent measurements, in such a way that the tension on the Hubble parameter can be alleviated.

Accelerated prediction of Vickers hardness of Co- and Ni-based superalloys from microstructure and composition using advanced image processing techniques and machine learning

Superalloys constitute an important class of materials that are heavily employed in turbines of aircraft engines and power plants. Vickers hardness is an important mechanical property for selection of a material. In this work, we develop an alternate approach, which uses the microstructures to estimate the hardness of a Co- and Ni- based superalloys. Advanced image processing techniques coupled with data-driven machine learning (ML) are used to predict the Vickers hardness of these superalloys. Complex image derived properties such as 2-point correlations and compositions of superalloys are utilized as a feature to develop highly accurate ML model. The ML model trained through Gaussian process regression (GPR) using microstructure and compositional features show unprecedented accuracy with root mean square error (RMSE) of 0.14 and R2 of 0.98. Further analysis of the model is done to establish a relationship between the Vickers hardness with microstructural and compositional parameters. Addition of certain compounds such as iron and titanium can in general lead to increase in Vickers hardness, while addition of elements such as aluminium, tantalum and hafnium negatively affect the Vickers hardness. Most importantly, the developed ML model is trained on experimental data, as opposed to simulated data, making our approach directly applicable for accurate prediction of Vickers hardness.

A digital workflow for learning the reduced-order structure-property linkages for permeability of porous membranes

Quantitative relationships between the complex porous structure of a membrane (henceforth simply referred to as microstructure) and its effective permeability are critical for improving the performance of membranes used in filtration and separation applications. This paper presents a digital workflow for learning the porous structure-permeability linkages in membranes. The presented workflow establishes the desired linkages by bringing together recent advances in (i) digital generators for three-dimensional representative volume elements (3-D RVEs) reflecting a large and diverse set of porous structures, (ii) numerical approaches for reliable evaluation of permeability of 3D-RVEs, (iii) low dimensional representation of material internal structure using the framework of 2-point spatial correlations and principal component analyses, and (iv) Gaussian process (GP) regression with input-dependent noise (i.e., heteroscedasticity). It is seen that the digital workflow presented in this study can systematically identify the salient features of the 3-D membrane microstructure and train reduced-order heteroscedastic GP models on the data generated using digital microstructure generators and physics-based permeability simulations. It will be shown that the structure-property linkages are able to make high fidelity predictions and assessment of uncertainties for new porous membrane structures at minimal computational cost.